Stochastic Analysis Seminar – Ashot Aleksian (Heriot Watt University)

This talk focuses on the exit-time problem of Freidlin and Wentzell. By exit time, we mean the first time a stochastic process reaches the boundary of a domain that is positively invariant (in a sense that will be clarified during the talk). We study this stopping time in the small-noise regime and discuss how the classical results on the exponential growth of the exit time—in probability and in expectation—can be obtained. We will also highlight the challenges that arise when extending these results beyond the standard assumptions of the Freidlin–Wentzell theory.

 As an example of such an extension, we will consider the McKean–Vlasov process, characterized by the interaction of the process with its own law at each point in time. We will show how the results of the Freidlin–Wentzell theory can be extended to the McKean–Vlasov setting and to other time-inhomogeneous processes.

 The talk is based on joint works with Julian Tugaut and Stéphane Villeneuve.